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Abstract

The following discloses a technique to use a Booth-encoded multiplier to produce the unsigned product of two unsigned operands.

Country

United States

Language

English (United States)

This text was extracted from an ASCII text file.

This is the abbreviated version, containing approximately
61% of the total text.

Multiplication of Unsigned Operands on a Booth-Encoded
Multiplier

The following
discloses a technique to use a Booth-encoded
multiplier to produce the unsigned product of two unsigned operands.

Hardware
multipliers generate partial products and then add
them together to get a final product.
When numbers are represented
in 2's complement notation, Booth-encoding can be used to reduce the
number of partial products required.
Reducing the number of partial
products reduces the amount of hardware required to implement the
multiply algorithm and improves the performance.

However, the
unsigned number format is inconsistent with 2's
complement format when the most significant bit is a '1'. In
unsigned number format, having the most significant bit set to a '1'
indicates that the number is a very large positive number. In 2's
complement format, having the most significant bit set to a '1'
indicates a negative number. For
unsigned numbers with the most
significant bit set to a '1', the Booth-encoded multiplier does not
provide the correct answer.

A
modification to a Booth-encoded multiplier has been made that
allows support of both unsigned and 2's complement numbers. The
modification recognizes that an unsigned number can be converted to
2's complement format by concatenating 0s to the most significant
bits of the unsigned number.
Specifically, a 32-bit unsigned number
can be converted to a 36-bit 2's complement number by con...